Finite Group Databasebeta

← #20253347

Subgroups — #20253347

Order 6016.

418 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 418 conjugacy classes of subgroups — too many to draw. Only its 133 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#15689687C211yesmaximal, characteristic
2#15689606C211yesmaximal, characteristic, complemented
3#15689448C212yesmaximal, complemented
4#15689448C212yesmaximal, complemented
5#15689442C212yesmaximal, complemented
6#15689437C212yesmaximal, complemented
7#15689165C211yesmaximal, characteristic, complemented
8#15689161C211yesmaximal, characteristic, complemented
9#15689129C211yesmaximal, characteristic, complemented
10C2×#13093946C211yesmaximal, characteristic, complemented
11C47×#408C211yesmaximal, characteristic, complemented
12C22×D188C2211yescharacteristic
13#13094020—21no—
14#13094013—21no—
15#13093998C2212yes—
16#13093998C2212yes—
17#13093992—22no—
18Q8×Dic47—21no—
19D4×Dic47—21no—
20D4×Dic47—22no—
21#13093983C2211yescharacteristic
22#13093983C2211yescharacteristic
23#13093983C2212yescomplemented
24C2×C4⋊Dic47C2211yescharacteristic
25C2×C4⋊Dic47C2212yescomplemented
26#13093958C2211yescharacteristic, complemented
27#13093958C2211yescharacteristic, complemented
28#13093958C2212yescomplemented
29#13093956C2211yescharacteristic, complemented
30#13093956C2211yescharacteristic, complemented
31#13093956C2212yescomplemented
32#13093946C2212yes—
33#13093946C2212yes—
34#13093946C2212yes—
35#13093946C2212yes—
36C2×#41×C47C2211yescharacteristic
37C2×M16×C47C2211yescharacteristic
38C22×C8×C47C2211yescharacteristic
39C22⋊C8×C47C2212yescomplemented
40C22⋊C8×C47C2212yescomplemented
41C23×D47—21no—
42#41×C47—22no—
43#41×C47—22no—
44C2×Q8×C47D411yescharacteristic
45C2×D4×C47D412yes—
46C2×D4×C47D411yescharacteristic
47C22×C4×C47C2312yes—
48C22×C4×C47C2311yescharacteristic
49C2×C22⋊D47—22no—
50C2×C22⋊D47—22no—
51C22×Dic47—21no—
52C22×Dic47—22no—
53C2×D188—22no—
54C2×D188—22no—
55C2×D188—21no—
56C2×D188C2312yes—
57M16×C47—22no—
58C2×C8×C47—22no—
59C2×C8×C47C2311yescharacteristic
60C2×C8×C47C2311yescharacteristic
61C2×C8×C47C2312yes—
62C22⋊Dic47—21no—
63C22⋊Dic47—21no—
64C22⋊Dic47—22no—
65(C2×D47)⋊C4—22no—
66(C2×D47)⋊C4—22no—
67C4⋊Dic47—21no—
68C4⋊Dic47—22no—
69C4⋊Dic47C2312yes—
70C4⋊Dic47C2311yescharacteristic
71C4⋊Dic47C2311yescharacteristic
72C4⋊Dic47C2311yescharacteristic
73C4⋊Dic47C2311yescharacteristic
74C4×Dic47—21no—
75C4×Dic47—21no—
76C4×Dic47—22no—
77C23×C47C2×D412yes—
78C23×C47C2×D411yescharacteristic
79C22×D47—22no—
80C22×D47—42no—
81C22×D47—81no—
82C22×D47—81no—
83Q8×C47—22no—
84D4×C47—24no—
85D4×C47—22no—
86C2×C4×C47—22no—
87C2×C4×C47—22no—
88C2×C4×C47C2×D412yes—
89C2×C4×C47C2×D411yescharacteristic
90C2×C4×C47#4112yes—
91C2×C4×C47#4112yes—
92C2×C4×C47C2411yescharacteristic
93C22⋊D47—82no—
94C22⋊D47—82no—
95C2×Dic47—21no—
96C2×Dic47—21no—
97C2×Dic47—22no—
98C2×Dic47—21no—
99C2×Dic47—21no—
100C2×Dic47—81no—
101C2×Dic47—82no—
102D188—22no—
103D188—22no—
104D188—42no—
105C8×C47—21no—
106C8×C47—21no—
107C8×C47—22no—
108C22×C47—21no—
109C22×C47—21no—
110C22×C47—22no—
111C22×C47—22no—
112C22×C47—22no—
113C22×C47#12312yes—
114C22×C47C22×D411yescharacteristic
115C2×D47—42no—
116C2×D47—42no—
117C2×D47—42no—
118C2×D47—84no—
119C4×C47—22no—
120C4×C47#12312yes—
121C4×C47C2×#4111yescharacteristic
122C4×C47C2×#4111yescharacteristic
123Dic47—41no—
124Dic47—42no—
125Dic47—41no—
126Dic47—41no—
127Dic47—41no—
128#3096—471nomaximal, Sylow
129C2×C47—22no—
130C2×C47—42no—
131C2×C47C2×#12311yescharacteristic
132C2×C47#57611yescharacteristic
133C2×C47#57711yescharacteristic
134D47—82no—
135#535—471no—
136#520—471no—
137#482—472no—
138#482—472no—
139#481—472no—
140#480—472no—
141#428—471no—
142#427—471no—
143#418—471no—
144C2×#102—471no—
145#408D4711yescharacteristic, complemented
146C47#309611yescharacteristic, complemented, Sylow
147C2×#41C2×D4711yescharacteristic
148C22×D4—471no—
149C2×M16C2×D4711yescharacteristic
150C22×C8C2×D4711yescharacteristic
151#127—941no—
152#124—941no—
153#121—472no—
154#121—472no—
155#120—942no—
156C4×Q8—941no—
157C4×D4—942no—
158C4×D4—941no—
159#117—471no—
160#117—472no—
161#117—471no—
162C2×C4⋊C4—471no—
163C2×C4⋊C4—472no—
164#107—471no—
165#107—471no—
166#107—472no—
167#106—471no—
168#106—471no—
169#106—472no—
170#102—472no—
171#102—472no—
172#102—472no—
173#102—472no—
174C22⋊C8C2×D4712yescomplemented
175C22⋊C8C2×D4712yescomplemented
176C24—941no—
177#41—22no—
178#41—22no—
179C2×Q8D18811yescharacteristic
180C2×D4—472no—
181C2×D4—942no—
182C2×D4—942no—
183C2×D4—941no—
184C2×D4—942no—
185C2×D4—942no—
186C2×D4D18812yes—
187C2×D4D18811yescharacteristic
188C22×C4—942no—
189C22×C4—941no—
190C22×C4C22×D4712yes—
191C22×C4C22×D4711yescharacteristic
192M16—22no—
193C2×C8—22no—
194C2×C8C22×D4711yescharacteristic
195C2×C8C22×D4712yes—
196C2×C8C22×D4711yescharacteristic
197C4⋊C4—472no—
198C4⋊C4—471no—
199C4⋊C4—471no—
200C4⋊C4—471no—
201C4⋊C4—471no—
202C4⋊C4—942no—
203C4⋊C4—941no—
204C22⋊C4—942no—
205C22⋊C4—941no—
206C22⋊C4—941no—
207C22⋊C4—942no—
208C22⋊C4—942no—
209C42—942no—
210C42—941no—
211C42—941no—
212C23—942no—
213C23—3761no—
214C23—3761no—
215C23—1882no—
216C23C2×D18812yes—
217C23C2×D18811yescharacteristic
218Q8—22no—
219D4—24no—
220D4—22no—
221D4—942no—
222D4—942no—
223D4—3762no—
224D4—3762no—
225D4—1882no—
226C2×C4—22no—
227C2×C4—22no—
228C2×C4—941no—
229C2×C4—941no—
230C2×C4—941no—
231C2×C4—941no—
232C2×C4—942no—
233C2×C4—3761no—
234C2×C4—3762no—
235C2×C4C2×D18812yes—
236C2×C4C2×D18811yescharacteristic
237C2×C4#1062535212yes—
238C2×C4#1062535212yes—
239C2×C4C23×D4711yescharacteristic
240C8—21no—
241C8—21no—
242C8—22no—
243C22—21no—
244C22—21no—
245C22—22no—
246C22—22no—
247C22—22no—
248C22—3764no—
249C22—1882no—
250C22—1882no—
251C22—1882no—
252C22#1309400812yes—
253C22C22×D18811yescharacteristic
254C4—22no—
255C4—1882no—
256C4—1881no—
257C4—1881no—
258C4—1881no—
259C4—1881no—
260C4#1309400812yes—
261C4C2×#1062535211yescharacteristic
262C4C2×#1062535211yescharacteristic
263C2—22no—
264C2—42no—
265C2—3762no—
266C2C2×#1309400811yescharacteristic
267C2#1568992811yescharacteristic
268C2#1568993511yescharacteristic
subgroupG/H
centerC22C22×D188
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#408C2
socleC22×C47C22×D4
hypercenter#408D47
hypocenterC47#3096
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×#41 ◁ #408

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #15689606C2semidirect
3. #15689448C2semidirect
4. #15689448C2semidirect
5. #15689442C2semidirect
6. #15689437C2semidirect
7. #15689165C2semidirect
8. #15689161C2semidirect
9. #15689129C2semidirect
10. C2×#13093946C2semidirect
11. C47×#408C2semidirect
23. #13093983C22semidirect
25. C2×C4⋊Dic47C22semidirect
26. #13093958C22semidirect
27. #13093958C22semidirect
28. #13093958C22semidirect
29. #13093956C22semidirect
30. #13093956C22semidirect
31. #13093956C22semidirect
39. C22⋊C8×C47C22semidirect
40. C22⋊C8×C47C22semidirect
145. #408D47semidirect
146. C47#3096semidirect
174. C22⋊C8C2×D47semidirect
175. C22⋊C8C2×D47semidirect